Golf game computer including improved drag circuit

ABSTRACT

A golf game computer including a circuit for computing the instantaneous velocity of a golf ball hit from a tee and including a circuit operative to receive a signal representative of the initial velocity of a golf ball hit from a tee and apply thereto, the effect of drag. In the exemplary embodiment of the invention, a plurality of electrically parallel circuits, each having a switch therein, are utilized to provide a signal proportional to the mathematical square of the instantaneous velocity which is used in computation.

nite States Patent [72] Inventor James W. Sanders 3,506,810 4/1970 Katell 235/197 X Grand Haven, Mich. 3,194,562 7/1965 Speiser 273/184 [21] Appl. No. 1,188 3,501,152 3/1970 Conklin et a1. 273/185 X [22] Filed Jan. 7,1970 3,523,689 8/1970 Cornell eta]. 73/379 X [45] Patented Jan. 4, 1972 3,513,301 5/1970 Howe 235/197 X [73] Assignee Brunswick Corporation 3,523,195 8/1970 Thomas et al. 235/197 X Primary ExaminerEugene G. Botz 54 com GAME COMPUTER INCLUDING 488mm [IMPROVED DRAG CIRCUIT Attorney-Hofgren, Wegner, Allen, Stellman & McCord 2 Claims, 3 Drawing Figs.

[52] U.S.Cl 235/151, ABSTRACT: A golf game computer including a circuit for 73/379, 273/184, 235/151.32 computing the instantaneous velocity of a golf ball hit from a [51] int. Cl "G06! 15/44, tee and including a circuit operative to receive a signal G011 5/02 representative of the initial velocity of a golf ball hit from a tee [50] Field of Search 235/151, and apply thereto, the effect of drag. In the exemplary em- 151.32, 197; 273/184-185; 73/13, 379 bodiment of the invention, a plurality of electrically parallel circuits, each having a switch therein, are utilized to provide a References Cited signal proportional to the mathematical square of the instan- UNITED STATES PATENTS taneous velocity which is used in computation. 3,513,707 5/1970 Russell et a1 73/379 18\ r 7 7 m.- va m J, 5 rpm-' 5) BINARY D/fl 5. cuecu/r \l (7 Ml/lT/PLIER 5p, SPIN lxll 10 12 COUNTER can/meme v MAN 5 FOR5'PIN 474' vflocm/ DISPLACEMENT (muff) DURING SPIN 3 BOUNCE HOOK FORCE 3P/N sue: nvr uvr 5 46 14 2 0 42 49 2 ELEV/3770A! Fl t'z'os 8 MN 2 auonzmr 0 HNQE I??? 7? INV v flZ/MUT/l 14 Free m nr fi G Z6 z 0956 r 52 flZ/MUT/l Vi c030 s/NB relsm/onsrm' "x" VELOCITY 50 +5 Aug/X V4 cos 9 0055 Z :7 2" vELoclrf 4 I 62 "Y'vEwc/n V 5/N9 urrmva L/rr mvp 5 GMwrr FQAC! G/Eq wrY VELOCITY J z/rr Gmwrr 03 72 E Bowl/F ;"'VL0c/TY {4/ f i a slssaLooz PATENIEU Jul 4:972

SHEET 2 OF 3 QZQ slssaooir PATENTED JAN 4 SHEET 3 BF 3 BACKGROUND OF THE INVENTION The recent upsurge in the popularity of the game of golf has resulted in severe overcrowding of existing facilities. As a result, a number of proposals for indoor golf games which would enable the golfer to play the game year around and which would require much less space than outdoor courses have evolved.

A number of such proposals have been commercialized and of those commercialized, some are extremely sophisticated and provide a quite realistic simulation of the game of golf played on an outdoor course. Of course, in order to effect a realistic simulation, a variety of factors must be taken into consideration by the computational systems employed. One such factor is the effect of drag on a golf ball in flight.

One commercialized golf game includes means for considering the effect of drag on'a golf ball in flight in the course of computation of a balls theoretical trajectory. Specifically employed is an analog circuit arranged to implement a mathematical equation relating to the instantaneous velocity of a ball in flight to the initial velocity and which requires a signal proportional to the square of the instantaneous velocity. To provide such a signal, a signal representing the instantaneous velocity was applied to a voltage dependent resistor which permitted the current to pass therethrough at a rate that was intended to approximate the square of the voltage applied across the resistor.

While this circuit worked well for its intended purpose, a lack of uniformity from one voltage dependent resistor to another resulted in each computational system having quite different computational characteristics from the others and which could not be predicted with a reasonable degree of certainty in advance. Accordingly, painstaking adjustment of the circuit was required for each such computational system.

SUMMARY OF THE INVENTION It is the principal object of the invention to provide a new and improved golf game computer. More specifically, it is an object of the invention to provide a golf game computational system including an improved drag circuit which may be fabricated uniformly for each computational system thereby obviating the need for extensive adjustment of each system due to lack of uniformity of parts of the circuit.

The exemplary embodiment of the invention accomplishes the foregoing objects by means of a plurality of parallel circuits which are impressed with a signal having a voltage proportional to the instantaneous velocity of a golf ball at any time in flight. Each circuit includes an impedance in the form of a resistor and a switching means in the form of a semiconductor, and more specifically, a diode, having a predetermined breakover voltage. Biasing means are employed with each of the parallel circuits so as to control the firing point of each diode in relation to the voltage representing the instantaneous velocity and each of the resistors are chosen to provide a particular linear rate of increased current flow for a linear increase in the voltage representing instantaneous velocity.

The combination of the parallel circuits operate in concert so that for a low instantaneous velocity representing voltage, perhaps but one circuit will be conducting and, as the voltage is increased, additional circuits will sequentially begin to conduct. As more and more of the circuits begin to conduct, the total current flow through all circuits increases and by choosing the impedances properly, a curve of the total current flow versus the instantaneous velocity representing voltage may be made to accurately approximate an exponential relation and specifically, a mathematical square relation, to thereby provide a signal having a characteristic representative of the square of the instantaneous velocity.

Other objects and advantages will become apparent from the following specification taken in conjunction with the accompanying drawings.

DESCRIPTION OF THE DRAWINGS FIG. I is a block diagram of a golf game computing system in which an improved drag circuit made according to the invention may be employed; and

FIG. 2 is comprised of FIGS. 2A and 28 with FIG. 28 being adapted to be placed at the lower margin of FIG. 2A and illustrates a preferred embodiment of the improved drag circuit.

DESCRIPTION OF THE PREFERRED EMBODIMENT One form of golf game computer in which the inventive improvement constituting this invention is susceptible to use is basically that disclosed in the copending application of Russell et al., Ser. No. 588,922, filed Oct. 24, 1966, now U.S. Pat. No. 3,513,707, and assigned to the same assignee as the instant ap' plication, the details of which are incorporated herein by reference.

Before proceeding with the discussion of the basic operation of the computer, it is to be understood that the same computes, throughout the theoretical time of flight (including bouncing and rolling) of the ball, three coordinates of the ball in space. The coordinates represent the displacement of the ball in three directions from the tee point and, as is known in the art, are referred to as the X, Y and Z directions. The Y-direction is vertical and thus, the instantaneous Y-displacement represents the height of the ball in flight above the ground. The Z-direction is horizontal and straightaway from the tee point so that the instantaneous Z-displacement represents the distance of the ball from the tee point in a direction straightaway therefrom. The X-direction is also horizontal and is transverse to the Z-direction. Thus, the instantaneous X-displacement represents the location of the ball to either side of the line defining the Z-direction. Further, since the displacement can be to either side of the Z-direction, it may be either positive or negative while the Y- and Z-displacements will always be positive or zero.

The computer is illustrated in block form in FIG. I and includes a tee trigger 10 which is adapted to sense when a ball has been hit by a golfer from a tee area to start a binary counter 12. The binary counter 12 is stopped when the ball has traveled a predetermined distance from the tee by any suitable means. For example, in the Russell et al., application, there is provided an arcuate arrangement of photocells for sensing the initial angle of elevation of the ball and when the ball passes through the photocell matrix, a signal is generated thereby to stop the binary counter. Alternatively, the predetermined distance may be set by the location of a target for stopping the ball such as that disclosed in the copending application of Conklin et al., Ser. No. 820,558, filed Apr. 30, 1969, now US. Pat. No. 3,591,184 and assigned to the same assignee as the instant application, the: details of which are herein incorporated by reference. When the latter system is used, the means contained within the target for sensing elevation angle may also be used to stop the binary counter.

In any event, elevation angle detecting means 14 are provided and the same, in addition to detecting the initial angle of elevation 6 of a ball hit from the tee, are operative to stop the binary counter 12.

The count contained in the binary counter 12 is inversely representative of the initial velocity V, of the ball hit from the tee. That is, the higher the count in the binary counter 12, the longer it will have taken for the ball to pass the predetermined distance from the tee point to the elevation angle detecting means 14 and thus, the slower will be its velocity.

The count contained in the binary counter 12 is then decoded by a digital to analog conversion matrix 116 which is operative to convert and invert the digital time quantity contained in the binary counter to an analog velocity quantity designated V for initial velocity. This information is then fed to a drag circuit I8 which is operative to ascertain from the initial velocity V,,, the instantaneous velocity V,- of the ball at any point in its theoretical time of flight.

The digital to analog converter 16 also provides a second V (bounce) signal to the drag circuit 16 which is operative to increase the drag or decay rate of the instantaneous velocity V, after the free flight of the ball has terminated and the same is bouncing or rolling on the ground.

Returning to the elevation angle detecting means, the same rovides a signal to an elevation trigonometry matrix 20 which has two outputs. On one output, there is placed a signal having a magnitude which is proportional to the product of the instantaneous velocity V, and the cosine of the initial angle of elevation of the shot, cos 0, or V, cos 6. On the other output, there is placed a signal having a magnitude proportional to the product of the instantaneous velocity V, and the sine of the initial angle of elevation of the shot, sin 6, or V, sin 6.

The system also includes a azimuth angle detecting means 22 for detecting the initial angle B of the shot with respect to the azimuth. The azimuth angle detecting means 22 may be in the form of the photocells disclosed by Russell et al. or incorporated in the target in the manner disclosed by Conklin et al. The azimuth angle information provided by the azimuth angle detecting means 22 is then fed to an azimuth trigonometry matrix 24.

The V, cos 6 output from the elevation trigonometry matrix 20 is fed through an inverter 26 as an input to the azimuth trigonometry matrix 24. The azimuth trigonometry matrix then converts the signal to be proportional to the product of the instantaneous velocity V,, the cosine of 6, and the sine of B, V, cos sin B, which, as will be appreciated from the reading'of the Russell et al. application, correspond to the instantaneous velocity of the ball in the so-called X-direction without regard to the effects of side spin.

The azimuth trigonometry matrix 24 also provides a second signal which corresponds to the product of the instantaneous velocity V,-, the cosine of 9 and the cosine of B, V, cos 0 cos B, which correspond to the instantaneous velocity of the ball in the so-called Z-direction.

The V, cos 6 cos B signal is then used as an input for an integrating circuit 28 which provides as an output, a signal proportional to the instantaneous displacement of the ball in the Z-direction, 5,. As shown in FIG. 1, such a signal is of negative polarity and, for purposes explained in the Russell et al. application, this signal is also fed to an inverter 30 which provides as an output the same signal but with the opposite polarity.

The V,- cos 0 sin B output of the azimuth trigonometry matrix 24 is fed as an input to a first inverter 32 which, in turn, provides an input to a second inverter 34. Shunting the inverter 34 is a pair of relay contacts 36 which are operative to cut the inverter 34 in or out of the circuit.

As described in the Russell et al., application, the output of the azimuth trigonometry matrix 24 is of the same polarity regardless of whether the ball is traveling to the left or right in the X-direction. However, means are also provided in association with the matrix 24 for distinguishing whether the ball is traveling to the left or the right and such means are employed to open or close the contacts 36 appropriately. For example, if the polarity of the output inverter 32 is arbitrarily such as to indicate that the ball is traveling to the right and, in fact, the ball was sensed as traveling to the left, the distinguishing means would leave the contacts 36 open so that the inverter 34 would provide a signal having an opposite polarity of that provided by the inverter 32 thereby indicating that the ball was in fact traveling to the left. 0n the other hand, if the ball was in fact traveling to the right, the distinguishing means would cause the contacts 36 to be closed to thereby shunt the inverter 34 to provide a signal having a polarity indicating that the ball was in fact traveling to the right.

The parallel combination of the contacts 36 and the inverter 34 is connected to a summing point 38 whereat the effect of side spin is also considered in determining total velocity in the X-direction. A second input to the summing point 38 is taken from the output of an integrator 40 which has its input connected to a summing point 42. The summing point 42 receives information from two sources. Firstly, the same receives information froma hook-slice matrix 44 which in turn receives information from a spin detector 46 which provides an indication of side spin on the ball. The spin detector 46 may be either of the forms disclosed by Russell et al. or that disclosed by Conklin et al. The hook-slice matrix 44 also receives an input from a circuit 48 which is representative of a power of the instantaneous velocity V, received from the drag circuit 18.

The hook-slice matrix 44 also provides an output to the azimuth trigonometry matrix 24 which in turn provides an output to an inverter 50 which is connected to the summing point 42. The reasons for the foregoing connections are not material to the invention but are explained in detail in the Russell et al. application. For purposes of this application, it is sufficient to note that at the summing point 42, there will be a signal having a magnitude indicative of spin force or spin acceleration.

This signal is then fed to the integrator 40 which provides an output having a magnitude characteristic of the velocity in the X-direction due to side spin which, in turn, is summed at the summing point 38 with the velocity in the X-direction due to the initial angle with respect to the azimuth B.

The resulting signal is then fed as an input to an integrator 52 which provides an output representative of the instantaneous displacement in the X-direction or 8,.

An output from the elevation trigonometry matrix having the signal V, cos 0 impressed thereon is utilized as an input to a gravity and lift circuit 54. The gravity and lift circuit 54 provides an input to an integrator 56 which is representative of the acceleration in the Y-direction due to the effects of lift and gravity on the golf ball in flight. The integrator 56 in turn converts this signal to a lift and gravity velocity signal which is fed to a bounce circuit 58 which, by the means disclosed by Russell et al., is ineffective while the ball is in free flight but comes into play when the ball would begin its bouncing or rolling along the ground.

The output of the bounce circuit 58 is in turn fed to a summing point 60 which receives the V, sin 0 output from the elevation trigonometry matrix 20 which is representative of the velocity in the Y-direction without regard to the effects of lift and gravity. At the summing point 60, the two signals are combined and the resulting signal is then fed as an input to an integrator 62 which provides an output representative of the instantaneous displacement in the Y-direction, 8,. Of course, when the ball has encountered the ground for the first time, a bounce signal will be impressed upon the summing point 60 by the bounce circuit 58 and until such time as the ball would be motionless.

The signals representative of the displacements in the X", Y and Z" directions, 8,, 8,, and 5 may be used as inputs to a display device such as a ball spot projector for displaying the flight of the ball to the golfer.

The inventive improvement herein resides specifically in the drag circuit 18 and may best be understood with reference to FIGS. 2A and 2B. The computation to be effected is as follows.

As disclosed in the Russell et al. application, for a golf ball in flight, it has been found that the instantaneous velocity bears the followingrelation to the initial velocity.

where:

V, is the instantaneous velocity,

V,, is the initial velocity, and

K is the drag coefficient.

Also as pointed out in the Russell et al. application, the value of K changes depending upon the instantaneous velocity of the ball. That is, for a ball at a high velocity, the airflow around the same will be in a turbulent state and thus K will have a relatively low value. However, when the instantaneous velocity is decreased due to drag to the point where the airflow about the ball is in a laminar state, the drag coefficient or K will have an increased value.

The means by which the computation is effected are as follows. According to the exemplary embodiment of the inven' tion, a signal having a negative polarity whose voltage is proportional to the initial velocity is fed from the digital to analog converter 16 to the drag circuit including an operational amplifier 70 in an inverting and summing circuit on a lead 72. The output of the operational amplifier 70 is connected to a summing point 74 having a lead 76 associated therewith. The lead 76 provides a positive signal whose voltage is proportional to the instantaneous velocity of the ball at any point in the theoretical flight thereof to the remainder of the computer as indicated in FIG. 1.

The summing point 74 is also connected to a plurality of parallel circuits 78, 79, 80, 81, 82, 83 and 84 of which the circuits 7803 each include a resistor 85 in series with a solid state diode 86. The circuit 84 merely consists of the resistor 05.

In the exemplary embodiment of the invention, the anode of each of the diodes 86 is connected to a respective resistor 85 and this junction is in turn connected through at least respective resistors 07 to a positive source of power. As illustrated in FIG. 2A, certain of the resistors 87 are in series with potentiometers 00 and/or temperature dependent resistors 89 which provide for temperature compensation of the overall circuit. The wipers of the potentiometers 88, where used, are also connected to the positive source ofpower.

The arrangement is such that the V, signal from the summing point 74 is converted by the circuits 78-84 to a signal whose current is proportional to the square of the instantaneous velocity. This function is accomplished in the following manner. Each of the diodes 86 has a redetermined forward breakover voltage as is well known in the art. That is, a predetermined voltage differential must exist between the cathode and the anode before the diode 86 will conduct. Typically, this forward breakover voltage is on the order of 0.6 volts.

The circuits 78-83 take advantage of this characteristic of the semiconductor diodes 86 to utilize the same as switching devices for respectively cutting in or cutting out one or more of the circuits 78-83 from the overall circuit.

Accordingly, the resistors 87 and the resistors 88 (if present) are selected so that the anode of the associated diode 86 is impressed with a biasing potential that will preclude any of the diodes 06 from conducting when the summing point 74 is at zero volts. For a positive voltage at the summing point 74, one or more of the diodes 86 may be caused to conduct. This will occur because, for a positive potential at the summing point 74, the potential at the junction between the anode of the diodes 86 and the associated resistor 85 will become more positive than would be the case if the summing point 74 were at zero volts.

When the resistive values indicated are used, the diodes 86 are sequentially rendered conductive as the potential at the summing point 74 goes increasingly positive. In the normal operation of the circuit, the summing point 74 will initially be at some positive potential dependent upon the initial velocity of the golf shot and will gradually decrease thereby causing the circuits 78-83 to sequentially cease conducting. Of course, the more of the legs 78-84 that are conducting, the higher will be the current level at the common junction of the cathodes of the diodes 86.

The resistors 85, according to the exemplary embodiment, are selected to essentially control the slope of the current flow curve. That is, the amount of current passing through any given one of the circuits 7883 in proportion to voltage at the summing point 74 will be essentially determined by the value of the resistors 85.

The foregoing circuit including the circuits 7884 is arranged so that the total current flow at the common junction of the cathodes of the diodes 86 and the line 92 connected thereto is proportional to the square of the voltage at the summing point 74.

The circuit achieves this relation as follows. Starting with a zero volt potential at the summing point 74, as the potential increases at, for example, a linear rate, one of the diodes 06 will begin to conduct and as the voltage increases, current flow will increase according to Ohms law at a linear rate. At some predetermined point, another one of the diodes 06 will begin to conduct and as a result, the current flow on the line 92 will be the sum of the current flow through the two circuit legs. While current flow in each of the two now conducting circuits will be linear according to voltage increase, total current flow would be represented by a linear upswing starting at the point when the second circuit begins to conduct and which would be equal to the sum of the current flow through the two conducting legs. This procedure will continue on until all of the circuits 78-03 are conducting.

A graph of the voltage to the summing point 74 versus total current flow on the line 92 would result in a series of short, straight line segments of differing slopes which would approximate an exponential curve and, more specifically, one of the general form of Y=x As a result, current flow along the line 92 will be closely proportional to the square of the voltage at the summing point 74.

The line 92 is connected as an input to an operational amplifier 94 in an inverting circuit as seen in FIG. 2B. The output signal of the operational amplifier 94 is placed on a line 96, is negative in polarity and its voltage is proportional to the square of the instantaneous velocity of "the ball.

Interconnecting the lines 92 and 96 are two parallel circuits 98 and 100 with the circuit 98 including a single resistor 102 and the circuit 100 including a resistor 104 and a diode 106. The two circuits 98 and 100 insert the K or drag coefficient into computation.

Specifically, it will be seen that whenever there is a potential difference between the lines 92 and 96, the circuit 98 will be conducting while the circuit 100 may not be, depending upon whether the forward breakover voltage of the diode 106 therein is exceeded.

The foregoing interconnections of the line 92 ultimately to the summing point 74 will result in the signal on the line 92 having a voltage which will be related to the instantaneous velocity of the ball. For high instantaneous velocities, the for ward breakover voltage of the diode 106 is exceeded and both the circuits 98 and 100 will be conducting and will result in a lesser rate of decay. However, through a biasing circuit 107, the diode 106 may be biased such that, when the instantaneous velocity of the ball falls to that value wherein ball flight would be accompanied by air flow in the laminar region, the diode 106 ceases conducting so that only the circuit 98 would be interconnecting the lines 92 and 96 to result in a higher rate of decay.

Returning to the line 96, the connection thereto may be utilized to provide a signal proportional to the square of the instantaneous velocity to the hook-slice matrix 44 as illustrated in FIG. 2B. When such is done, the spin multiplier 48 may be eliminated.

Also, the line 96 is connected to ground through a potentiometer 108 which may have the position of its wiper changed to correctly proportion the magnitude of the signal taken from the operational amplifier 94. The signal picked off the wiper of the potentiometer 108 is then fed through a resistive circuit 110 to the normally open contacts 112a of the relay 112. The relay 112 may be energized through leads 113 and 114 which may be connected into the Russell et al. computer in the manner described therein such that the relay 112 is energized when the computer initiates computation and is deenergized when the computer is reset. Accordingly, when the computer initiates computation, the relay 112 will be energized to close the contacts 112a and ultimately apply the signal from the potentiometer 108 as an input to an operational amplifier 115 in an integrating circuit.

Included in the integrating circuit associated with the operational amplifier 115 is an integrating capacitor 116 which has one lead connected to the input to the operational amplifier 115 and one lead connected to the output thereof. The relay 112 includes a pair of normally closed contacts 112!) which are connected through a load resistor 118 to the input and the output of the operational amplifier 115. When the computer is undergoing a computation cycle, the contacts 112 will be opened due to the energization of the relay 112. However, when computation is complete and the relay 112 deenergized, the contacts 112b will close thereby discharging the capacitor 116 through the resistor 118 so as to effectively reset the integrating circuit associated with the operational amplifier 115 to the next computation.

The output of the operational amplifier 115 is negative in polarity and is fed on a line 120 to the summing point 74 through resistors 122 and 124.

As mentioned in the Russell et al. application, it is desirable to increase the rate of drag when the ball is bouncing on the ground. To this end, there is provided a resistor 126 which has one side thereof connected to the input of the operational amplifier 115 during computation when the contacts 112a are closed and which has its other side connected to normally open contacts 128a of a relay 128. The outer side of the normally open contacts 128a is returned by a line 130 to the line 96.

The relay 128 includes a pair of leads 132 and 134 which are energized when the computer has determined that the ball touched the ground for the first time and which are maintained energized until the computer is reset. Suitable means for this purpose are disclosed in the Russell et al. application. Thus, at the first touch down of the ball, the relay 128 will be energized to thereby close the contacts 128a and this action effectively puts the resistor 126 in parallel with the resistor 108 to increase the rate of decay thereby effecting increasing drag during the bouncing or rolling of the ball on the ground.

Summarizing, a negative signal having a voltage proportional to the initial velocity is inverted and provided to the summing point 74 by the operational amplifier 70. At the initiation of the flight of the ball, the instantaneous velocity will equal the initial velocity with the result being that the highest positive potential for any given golf shot will be applied to the circuits 78, 79, 80, 81, 82, 83 and 84 which convert the signal to a signal proportional to the square of the instantaneous velocity which is then fed to the inverting operational amplifier 94. The operational amplifier 94 in turn provides a negative output signal having a voltage proportional to the square of the instantaneous velocity and which is diminished by the effect of the circuits 98 and 100 which provide for the introduction of the drag coefficient. The negative signal, as affected by drag, is then fed to the integrating operational amplifier 115 which then provides an output signal that is negative in polarity and proportional to the integral of the instantaneous velocity squared to the summing point 74. Since the initial velocity voltage at the summing point is positive, and the voltage provided by the integrating operational amplifier 115, which is representative ofthe term is negative, subtraction will result so that the output on the lead 76 is a positive signal proportional to the instantaneous velocity of the ball at any time in the theoretical flight thereof.

lclaim:

1. In a golf game including means for determining the initial representative thereof, the combination comprising: a first operational amplifier in an inverting circuit; means for feeding said initial velocity signal to said operational amplifier; a plurality of electrically parallel circuits, at least one of which consists of a resistance and the remainder each comprising a serial combination of a resistance and a semiconductor having a known breakover voltage; a plurality of biasing circuits, one for each of said remaining circuits and connected to its associated remaining circuit at the junction of said resistance and said semiconductor, at least some of said biasing circuits including temperature compensator means to provide for temperature compensation for the parallel circuits;

means connecting an output of said first operational amplifier to one side of each of said parallel circuits;

a second operational amplifier in an inverting circuit;

means connecting the opposite side of said parallel circuits to the input of said second operational amplifier;

a first resistance shunting said second operational amplifier;

a second resistance shunting said second operational amplifier;

means for controlling the conduction of said second resistance including a semiconductor having a predetermined breakover voltage in series therewith and a biasing circuit including a variable resistance connected to the junction of said last-named semiconductor and said second resistance;

a potentiometer including a wiper connected to the output of said second operational amplifier;

means defining a spin velocity function output terminal connected to the output of said second operational amplifier;

a relay including normally open contacts adapted to be closed when said relay is energized;

means conducting said potentiometer wiper to one side of said contacts;

a third operational amplifier in an integrating circuit and including a capacitor shunting said third operational amplifier;

means connecting the other side of said contacts as an input to said third operational amplifier;

said relay further including normally closed contacts shunting said third operational amplifier whereby, when said relay is deenergized, said capacitor will be discharged;

and means including a resistance connecting the output of said third operational amplifier to the output of said first operational amplifier to issue a signal proportional to the instantaneous velocity of a golf ball hit from a tee during the flight thereof.

2. The combination of claim 1 further including a second relay having normally open contacts and adapted to be energized when the theoretical free flight trajectory of a golf ball contacts the ground; means including a resistance interconnecting one side of said second relay contacts to said one side of the normally open contacts of said first-named relay; and means connecting the other side of said second relay contacts at least partially in parallel with said potentiometer whereby when the theoretical free flight of a golf ball causes the same to contact the ground, an increase in drag will be effected to increase the rate of decay of said instantaneous velocity signal during the bouncing and/or rolling of the ball on the ground. 

1. In a golf game including means for determining the initial velocity of a golf ball hit from a tee and providing a signal representative thereof, the combination comprising: a first operational amplifier in an inverting circuit; means for feeding said initial velocity signal to said operational amplifier; a plurality of electrically parallel circuits, at least one of which consists of a resistance and the remainder each comprising a serial combination of a resistance and a semiconductor having a known breakover voltage; a plurality of biasing circuits, one for each of said remaining circuits and connected to its associated remaining circuit at the junction of said resistance and said semiconductor, at least some of said biasing circuits including temperature compensator means to provide for temperature compensation for the parallel circuits; means connecting an output of said first operational amplifier to one side of each of said parallel circuits; a second operational amplifier in an inverting circuit; means connecting the opposite side of said parallel circuits to the input of said second operational amplifier; a first resistance shunting said second operational amplifier; a second resistance shunting said second operational amplifier; means for controlling the conduction of said second resistance including a semiconductor having a predetermined breakover voltage in series therewith and a biasing circuit including a variable resistance connected to the junction of said lastnamed semiconductor and said second resistance; a potentiometer including a wiper connected to the output of said second operational amplifier; means defining a spin velocity function output terminal connected to the output of said second operational amplifier; a relay including normally open contacts adapted to be closed when said relay is energized; means conducting said potentiometer wiper to one side of said coNtacts; a third operational amplifier in an integrating circuit and including a capacitor shunting said third operational amplifier; means connecting the other side of said contacts as an input to said third operational amplifier; said relay further including normally closed contacts shunting said third operational amplifier whereby, when said relay is deenergized, said capacitor will be discharged; and means including a resistance connecting the output of said third operational amplifier to the output of said first operational amplifier to issue a signal proportional to the instantaneous velocity of a golf ball hit from a tee during the flight thereof.
 2. The combination of claim 1 further including a second relay having normally open contacts and adapted to be energized when the theoretical free flight trajectory of a golf ball contacts the ground; means including a resistance interconnecting one side of said second relay contacts to said one side of the normally open contacts of said first-named relay; and means connecting the other side of said second relay contacts at least partially in parallel with said potentiometer whereby when the theoretical free flight of a golf ball causes the same to contact the ground, an increase in drag will be effected to increase the rate of decay of said instantaneous velocity signal during the bouncing and/or rolling of the ball on the ground. 